System, method and program for estimating risk of disaster in infrastructure

ABSTRACT

Method, system and computer program for estimating risk of a future disaster of an infrastructure. Times of previous, respective disasters of the infrastructure are identified. Respective severities of the previous disasters are determined. Risk of a future disaster of the infrastructure is estimated by determining a relationship between the previous disasters, their respective severities and their respective times of occurrence. The risk can be estimated by generating a polynomial linking severity and time of occurrence of each of the previous disasters. The polynomial can be generated by approximating a Tchebychev polynomial.

CROSS REFERENCE TO RELATED APPLICATION

This application is a Continuation application of copending U.S. Ser.No. 11/272,299 which was filed on Nov. 10, 2005, now Abandoned.

TECHNICAL FIELD

The present invention relates to estimation of disasters ininfrastructures, such as computer networks.

BACKGROUND

Risk analysis predicts likelihood of disasters, such as severe failuresof an Information Technology (“IT”) infrastructure, that an organizationmay face, and the consequences of such failures. IT disasters, such asan e-mail server failure or other computer network failure, can impactthe organization's ability to operate efficiently.

Known cindynic theory (science of danger) is applicable in differentdomains. For example, cindynics has been used to detect industrial risksand can also be used in the area of computer network (including computerhardware and software) risks. According to the modern theory ofdescription, a hazardous situation (cindynic situation) has been definedif the field of the “hazards study” is clearly identified by limits intime (life span), limits in space (boundaries), and limits in theparticipants' networks involved and by the perspective of the observerstudying the system. At this stage of the known development of thesciences of hazards, the perspective can follow five main dimensions.

A first dimension comprises memory, history and statistics (a space ofstatistics). The first dimension consists of all the informationcontained in databases of large institutions constituting feedback fromexperience (for example, electricity of France power plants, Air Franceflights incidents, forest fires monitored by the Sophia Antipolis centerof the Ecole des Mines de Paris, and claims data gathered by insurersand reinsurers).

A second dimension comprises representations and models drawn from thefacts (a space of models). The second dimension is the scientific bodyof knowledge that allows computation of possible effects using physicalprinciples, chemical principles, material resistance, propagation,contagion, explosion and geo-cindynic principles (for example,inundation, volcanic eruptions, earthquakes, landslides, tornadoes andhurricanes).

A third dimension comprises goals & objectives (a space of goals). Thethird dimension requires a precise definition by all the participantsand networks involved in the cindynic situation of their reasons forliving, acting and working. It is arduous to clearly express whyparticipants act as they do and what motivates them. For example, thereare two common objectives for risk management—“survival” and “continuityof customer (public) service”. These two objectives lead tofundamentally different cindynic attitudes. The organization, or itsenvironment, will have to harmonize these two conflicting goals.

A fourth dimension comprises norms, laws, rules, standards, deontology,compulsory or voluntary, controls, etc. (a space of rules). The fourthdimension comprises all the normative set of rules that makes lifepossible in a given society. For example, socient determined a need fora traffic code when there were enough automobiles to make it impossibleto rely on courtesy of each individual driver; the code is compulsoryand makes driving on the road reasonably safe and predictable. The rulesfor behaving in society are aimed at reducing the risk of injuring otherpeople and establishing a society. On the other hand, there aresituations, in which the codification is not yet clarified. For example,skiers on the same ski-slope may have different skiing techniques andendanger each other. In addition, some skiers use equipment notnecessarily compatible with the safety of others (cross country sky andmono-ski, etc.)

A fifth dimension comprises value systems (a space of values). The fifthdimension is the set of fundamental objectives and values shared by agroup of individuals or other collective participants involved in acindynic situation. For example, protection of a nation from an invaderwas a fundamental objective and value, and meant protection of thephysical resources as well as the shared heritage or values. Protectionof such values may lead the population to accept heavy sacrifices.

A number of general principles, called axioms, have been developedwithin cindynics. The cindynic axioms explain the emergence ofdissonances and deficits.

CINDYNIC AXIOM 1—RELATIVITY: The perception of danger varies accordingto each participant's situation. Therefore, there is no “objective”measure of danger. This principle is the basis for the concept ofsituation.

CINDYNIC AXIOM 2—CONVENTION: The measures of risk (traditionallymeasured by the vector Frequency—Severity) depend on convention betweenparticipants.

CINDYNIC AXIOM 3—GOALS DEPENDENCY: Goals can directly impact theassessment of risks. The participants may have conflicting perceivedobjectives. It is essential to try to define and prioritise the goals ofthe various participants involved in the situation. Insufficientclarification of goals is a current pitfall in complex systems.

CINDYNIC AXIOM 4—AMBIGUITY: There is usually a lack of clarity in thefive dimensions previously mentioned. A major task of prevention is toreduce these ambiguities.

CINDYNIC AXIOM 5—AMBIGUITY REDUCTION: Accidents and catastrophes areaccompanied by brutal transformations in the five dimensions. Thereduction of ambiguity (or contradictions) of the content of the fivedimensions will happen when they are excessive. This reduction can beinvoluntary and brutal, resulting in an accident, or voluntary andprogressive achieved through a prevention process.

CINDYNIC AXIOM 6—CRISIS: A crisis results from a tear in the socialcloth. This means a dysfunction in the networks of the participantsinvolved in a given situation. Crisis management may comprises anemergency reconstitution of networks.

CINDYNIC AXIOM 7—AGO-ANTAGONISTIC CONFLICT: Any therapy is inherentlydangerous. Human actions and medications are accompanied by inherentdangers. There is always a curing aspect, reducing danger(cindynolitic), and an aggravating factor, creating new danger(cindynogenetic).

The main utility of these principles is to reduce time lost inunproductive discussions on the following subjects:

-   -   How accurate are the quantitative evaluations of        catastrophes—Quantitative measures result from conventions,        scales or unit of measures (axiom 2); and    -   Negative effects of proposed prevention measures—In any action        positive and negative impacts are intertwined (axiom 7).

Consequently, Risk Analysis, viewed by the cindynic theory, takes intoaccount the frequency that the disaster appears (probability), and itsreal impact on the participant or organization (damage).

FIG. 1 shows a known “Farmer's” curve 9 where disasters are placed on agraph showing the relationship between probability and damage.

Disaster study is a part of Risk Analysis; its aim is to follow thedisaster evolution. Damages are rated in term of cost or rate, withtime. Let “d” denote the damage of a given disaster and “f” denote thefrequency of such a disaster. From a quantitative point of view, it iscommon to define a rating “R” of the associated risk as: R=d×f. Inpractice, often, the perception of risk is such that the relevance givento the damaging consequences “d” is far greater than that given to itsprobability of occurrence f so that, the given “R=d×f” is slightlymodified to: R=d^(k)×f with k>1. So, numerically larger values of riskare associated with larger consequences.

Disasters are normally identified by IT infrastructure components. Thesecomponents follow rules or parameters and may generate log traces.Typically, disaster information is represented in the form of log files.The disaster rating and scale are relative rather than absolute. Thescale may be, for example, values between “1” and “10”: “1” being aminor disaster of minimal impact to the disaster data group and “10”being a major disaster having widespread impact. The logging functiondepends of the needs of monitoring systems and data volumes and, in somecases, delay due to legal obligations.

The known Risk Analysis uses a simple comparison between values found bythe foregoing operations, in order to extract statistics. Also, a fullRisk Analysis of a IT infrastructure required a one to one analysis ofall the data held on disasters. By comparing each disaster with each ofthe other disaster it was possible to calculate the likelihood offurther disasters. This process is computationally expensive and alsorequires a significant amount of a computer's Random Access Memory(RAM).

An object of the present invention is to estimate risk of disaster of aninfrastructure.

Another object of the present invention is to facilitate estimation ofrisk of disaster of an infrastructure.

SUMMARY OF THE INVENTION

The present invention is directed to a method, system and computerprogram for estimating risk of a future disaster of an infrastructure.Times of previous, respective disasters of the infrastructure areidentified. Respective severities of the previous disasters aredetermined. Risk of a future disaster of the infrastructure is estimatedby determining a relationship between the previous disasters, theirrespective severities and their respective times of occurrence.

In accordance with a feature of the present invention, the risk isestimated by generating a polynomial linking severity and time ofoccurrence of each of the previous disasters. The polynomial can begenerated by approximating a Tchebychev polynomial.

In accordance with other features of the present invention, the risk isalso estimated by modifying the polynomial by extracting peaks in acurve representing the polynomial, regenerating the polynomial using theextracted peaks and repeating the modifying step until a number ofextracted peaks is less than or equal to a predetermined value.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of a prior art Farmer's curve.

FIG. 2 illustrates the result of the Tchebychev's polynomialsapproximation's use.

FIG. 3a illustrates a polynomial curve showing the collected disasterinformation from a first origin.

FIG. 3b illustrates a polynomial curve showing the collected disasterinformation from a second origin.

FIG. 4 illustrates the combining of the polynomial curves of FIG. 3according to an embodiment of the invention.

FIG. 5 is a flow diagram, including a flowchart and a block diagram,illustrating a program and system for generating polynomials accordingto the present invention.

FIG. 6 illustrates a system according to the present invention forestimating risk of disaster of an infrastructure.

DETAILED DESCRIPTION OF THE INVENTION

The present invention will now be described in detail with reference tothe Figures. A Tchebychev analysis program 500 (shown in FIGS. 5 and 6)executing in a risk estimation computer 20 generates a continuouspolynomial curve with a corresponding polynomial equation. Program 500takes derivatives of the polynomial equation. When the derivative of thecontinuous curve is null, the risk reaches its maximum. The constructionof the polynomial equation is shown below.

For i≧1 and j≧1, a Tchebychev polynomial having “n” points is given by:

${P_{n}(x)} = {\sum\limits_{i = 1}^{n}\left( {y_{i}{\prod\limits_{j = 1}^{n}\frac{\left( {x - x_{j}} \right)}{\left( {x_{i} - x_{j}} \right)}}} \right)}$For example, to calculate the polynomial between two points, Point1 andPoint2, having coordinates (x₁, y₁) and (x₂, y₂) respectively in space(x,y), the formula is: n=2,

${P_{2}(x)} = {{y_{1}\frac{\left( {x - x_{2}} \right)}{\left( {x_{1} - x_{2}} \right)}} + {y_{2}\frac{\left( {x - x_{1}} \right)}{\left( {x_{2} - x_{1}} \right)}}}$Where P₂ (x₁)=y₁, and P₂ (x₂)=y₂.To calculate the polynomial between 3 points: Point1 (x1, y1), Point2(x2,y2) and Point3 (x3,y3), the formula is: n=3,

${P_{3}(x)} = {{y_{1}\frac{\left( {x - x_{2}} \right)\left( {x - x_{3}} \right)}{\left( {x_{1} - x_{2}} \right)\left( {x_{1} - x_{3}} \right)}} + {y_{2}\frac{\left( {x - x_{1}} \right)\left( {x - x_{3}} \right)}{\left( {x_{2} - x_{1}} \right)\left( {x_{2} - x_{3}} \right)}} + {y_{3}\frac{\left( {x - x_{1}} \right)\left( {x - x_{2}} \right)}{\left( {x_{3} - x_{1}} \right)\left( {x_{3} - x_{1}} \right)}}}$where P₃(x₁)=y₁, P₃(x₂)=y₂ and P₃(x₃)=y₃.The Tchebychev polynomial is a continuous curve between “n” points.

Referring to FIG. 5, Tchebychev analysis program 500 receives identifieddisasters data 510 from an infrastructure which are then inputted to aTchebychev approximation module 520. The Tchebychev module 520calculates a polynomial from the identified disasters data 510. Thepolynomial is inputted to a derivative module 530. The derivative module530 identifies peaks and troughs by identifying points which have a nullderivative. The peaks having a null derivative are forwarded to a peaks(or tops) module 540. The peaks module 540 identifies the peaks bystudying the sign of the derivative before and after each of theidentified points. Where the sign of the derivative is positive beforeand negative after an identified point, a peak has been found. A newfilter module 550 counts the number of identified peaks and comparesthis to a predetermined maximum. If there are more identified peaks thanthe maximum, the identified peaks are inputted to the Tchebychev module520 and the process is repeated. If the number of peaks is less than orequal to the maximum the process stops (step 560).

FIG. 2 illustrates an example of results produced by program 500. Anidentified disasters trace 210 plots severity of a disaster againsttheir time of occurrence. Program 500 then generates an approximation ofTchebychev's polynomials to obtain a first polynomial equationrepresented by a first polynomial curve 220. Program 500 then takesderivatives of first polynomial equation 220 to identify the points atwhich the derivative is equal to zero. Null derivative points 230correspond to peaks and troughs on the polynomial curve. Program 500identifies peaks by analyzing each null derivative point 230. If thepolynomial values of the polynomial 220 before and after each nullderivative point 230 are lower that the peak polynomial value at thispoint, a peak is identified. In this example, program 500 alsoidentifies the extracted peaks 240 from the polynomial 220 throughcomparison with the identified disasters trace 210. Where a nullderivative point 230 is identified as a peak, program 500 compares thenull derivative point 230 to the value of identified disasters trace 210before and after the null derivative point 230. Thus, program 500identifies the extracted peaks 240 in FIG. 2. For example, point A isone of extracted peaks 240, B is the null derivative point 230 precedingA, and C is the null derivative point 230 following A. If the derivativeis positive between A and B, and negative between A and C, point A is apeak. Furthermore, the values of the identified disasters trace 210before and after point A are less than point A. Therefore point A is anextracted peak 240.

Program 500 then uses an approximation of Tchebychev's polynomials tocreate a modified polynomial 250 using points which have been identifiedas peaks and the start and end point. Program 500 further modifiespolynomial 250 by repeating the process described above to identifypeaks. In this case, there would be no further improvement but in othercases the process will preserve only the highest peaks.

Referring now to FIGS. 3a and 3b , polynomial curves 340 a and 340 bshow two collections of disaster information for two organizations(called “first origin” and “second origin”) with each disaster 310 a and310 b shown as a point (resembling a small circle) on the respectivepolynomial curve 340 a and 340 b. Program 500 identifies representedpeaks 320 a and 230 b (shown as starts) by the process described aboveto identify peaks from recovered data points. Each polynomial curve 340a and 340 b has respective ends 330 a and 330 b (shown as triangles).

Referring now to FIG. 4, the polynomial curves 450 a and 450 b representthe two polynomial curves 340 a and 340 b respectively, of FIGS. 3a and3b (340). The first origin of curve 450 a has disaster points 420(represented by the number “2” in a circle) and the second origin ofcurve 450 b has disaster points 430 (represented by the number “1” in acircle). Program 500 identifies peaks and ends of each of the polynomialcurves 450 a and 450 b, and extracts represented peaks. The new ends 440are the ends from either of the polynomial curves 450 a or 450 b whichare of greater gravity or greater extremity of time. Program 500 thenuses the represented peaks from each polynomial curve 450 a or 450 balong with the new ends 440 to generate a merged polynomial 460 whichrepresents disaster from the combined information of the first andsecond origin.

Referring now to FIG. 6, a data logger 602 which enables information,typically consisting of logged events, to be collected from ainfrastructure network 604. The information from the data logger 602 isstored in a data storage 606. A disaster identification program 608assesses the logged events to determine whether the event is deemed adisaster. For example, if the logged event indicates a failure of systemhardware or software it may be logged as a disaster. A disaster gravityprogram 610 assesses each identified disaster generating disaster data.For example, as described previously, a disaster may be assigned a valuebetween “1” and “10” corresponding to level of impact on theinfrastructure 604. The disaster data is then inputted to Tchebychevanalysis program 500 as described previously. The Tchebychev analysisprogram generates a risk analysis equation or data. Program 500 thenanalyzes the risk analysis data to identify one or more high riskdisaster events. For example, after the Tchebychev analysis program 500has completed the risk analysis, program 500 typically identifies anumber of peaks corresponding to high risk events 612. Thesepeaks/events can be identified as disasters which generate significantrisk to the infrastructure 604. Measures can then be automatically, orotherwise, taken to minimise further risk. For example, the computersystem 20 could instigate additional services on other computers orserver of the network 604 to provide additional redundancy to cope witha particular high risk event. The high risk events 612 can also bedisplayed on a computer screen, or any type of visual display unit, toallow a user to view and obtain more information about the high riskevents 612. In this manner, a disaster of greatest potential risk can beidentified automatically.

The present invention may be embodied in a computer program (includingprogram modules 608, 610, 500 and 612) comprising instructions which,when executed in computer 20, perform the functions of the system ormethod as described above. The computer 20 includes a standard CPU 12,operating system 14, RAM 16 and ROM 18. The program modules 608, 610,500 and 612 are stored on computer readable disk storage 606 forexecution by CPU 12 via computer readable memory 16. The program modules608, 610, 500 and 612 can be loaded into computer 20 from acomputer-readable storage device such as a magnetic disk or tape,optical device or DVD, or alternatively downloaded via network 604 via aTCP/IP adapter card 21.

Improvements and modifications may be incorporated without departingfrom the scope of the present invention.

What is claimed is:
 1. A method of estimating risk of a future failureof first and second computer systems of a computer network and takingremedial action which minimizes the risk of the future failure of thefirst and second computer systems, the method comprising: a processoridentifying, as first coordinates of first data points, (a) severitiesof previous, respective failures of the first computer system and (b)respective times of occurrences, encompassing a time range from anearliest time of occurrence T1min to a latest time of occurrence T1max,of the previous, respective failures of the first computer system,wherein the severities are the first coordinates on a severity axis andthe respective times of the occurrences are the first coordinates on aperpendicular time axis; the processor generating a first Tchebychevpolynomial curve passing through all of the first data pointsrepresenting the previous failures of the first computer system, andidentifying peaks and ends of the first Tchebychev polynomial curve; theprocessor identifying, as second coordinates of second data points, (a)severities of previous, respective failures of the second computersystem and (b) respective times of occurrences, encompassing a timerange from an earliest time of occurrence T2min to a latest time ofoccurrence T2max, of the previous, respective failures of the secondcomputer system, wherein the severities are the second coordinates onthe severity axis and the respective times of the occurrences are thesecond coordinates on the perpendicular time axis; the processorgenerating a second Tchebychev polynomial curve passing through all ofthe second data points representing the previous failures of the secondcomputer system, and identifying peaks and ends of the second Tchebychevpolynomial curve; and the processor generating a third Tchebychevpolynomial curve passing through: (i) all of the peaks of both the firstTchebychev polynomial curve and the second Tchebychev polynomial curve,(ii) the first Tchebychev polynomial curve at time T1min or the secondTchebychev polynomial curve at time T2min, and (iii) the firstTchebychev polynomial curve at time T1max or the second Tchebychevpolynomial curve at time T2max; and the processor identifying a highestpeak of the third Tchebychev polynomial curve and determining that theidentified highest peak is a high risk failure that occurred on thefirst or second computer system and is a disaster generating significantrisk to the computer network and in response, causing other computers ofthe computer network to provide additional redundancy to minimize thesignificant risk to the computer network from a future occurrence of thehigh risk failure of the first and second computer systems.
 2. Themethod of claim 1, the method further comprising: the processoridentifying an additional failure of the first computer system, theadditional failure occurring within a predetermined time period of oneof the failures of the first computer system, a severity of the onefailure of the first computer system being greater than a severity ofthe additional failure; and the processor determining not to use theadditional failure as a data point for generating the first Tchebychevpolynomial based on (a) the additional failure occurring within thepredetermined time of the one failure of the first computer system and(b) the severity of the one failure of the first computer system beinggreater than the severity of the additional failure.
 3. The method ofclaim 1, wherein the first computer system comprises a first network offirst computers including first software installed in the firstcomputers and wherein the second computer system comprises a secondnetwork of second computers including second software installed in thesecond computers.
 4. The method of claim 1, wherein if time T1min isless than time T2min then the third Tchebychev polynomial curve passesthrough the first Tchebychev polynomial curve at time T1min; wherein iftime T2min is less than time T1min then the third Tchebychev polynomialcurve passes through the second Tchebychev polynomial curve at timeT2min; wherein if time T1min is equal to time T2min then the thirdTchebychev polynomial curve passes through whichever Tchebychevpolynomial curve of the first and second Tchebychev polynomial curveshas a higher severity at time T1min; wherein if time T1max is greaterthan time T2max then the third Tchebychev polynomial curve passesthrough the first Tchebychev polynomial curve at time T1max; wherein iftime T2max is greater than time T1max then the third Tchebychevpolynomial curve passes through the second Tchebychev polynomial curveat time T2max; wherein if time T1max is equal to time T2max then thethird Tchebychev polynomial curve passes through whichever Tchebychevpolynomial curve of the first and second Tchebychev polynomial curveshas a higher severity at time T1max.
 5. A computer program product,comprising a computer readable hardware storage device having computerreadable program instructions stored therein, said program instructionsexecutable by a processor to implement a method of estimating risk of afuture failure of first and second computer systems of a computernetwork and taking remedial action which minimizes the risk of thefuture failure of the first and second computer systems, the methodcomprising: the processor identifying, as first coordinates of firstdata points, (a) severities of previous, respective failures of thefirst computer system and (b) respective times of occurrences,encompassing a time range from an earliest time of occurrence T1min to alatest time of occurrence T of the previous, respective failures of thefirst computer system, wherein the severities are the first coordinateson a severity axis and the respective times of the occurrences are thefirst coordinates on a perpendicular time axis; the processor generatinga first Tchebychev polynomial curve passing through all of the firstdata points representing the previous failures of the first computersystem, and identifying peaks and ends of the first Tchebychevpolynomial curve; the processor identifying, as second coordinates ofsecond data points, (a) severities of previous, respective failures ofthe second computer system and (b) respective times of occurrences,encompassing a time range from an earliest time of occurrence T2min to alatest time of occurrence T2max, of the previous, respective failures ofthe second computer system, wherein the severities are the secondcoordinates on the severity axis and the respective times of theoccurrences are the second coordinates on the perpendicular time axis;the processor generating a second Tchebychev polynomial curve passingthrough all of the second data points representing the previous failuresof the second computer system, and identifying peaks and ends of thesecond Tchebychev polynomial curve; and the processor generating a thirdTchebychev polynomial curve passing through: (i) all of the peaks ofboth the first Tchebychev polynomial curve and the second Tchebychevpolynomial curve, (ii) the first Tchebychev polynomial curve at timeT1min or the second Tchebychev polynomial curve at time T2min, and (iii)the first Tchebychev polynomial curve at time T max or the secondTchebychev polynomial curve at time T2max; and the processor identifyinga highest peak of the third Tchebychev polynomial curve and determiningthat the identified highest peak is a high risk failure that occurred onthe first or second computer system and is a disaster generatingsignificant risk to the computer network and in response, causing othercomputers of the computer network to provide additional redundancy tominimize the significant risk to the computer network from a futureoccurrence of the high risk failure of the first and second computersystems.
 6. The computer program product of claim 5, the method furthercomprising: the processor identifying an additional failure of the firstcomputer system, the additional failure occurring within a predeterminedtime period of one of the failures of the first computer system, aseverity of the one failure of the first computer system being greaterthan a severity of the additional failure; and the processor determiningnot to use the additional failure as a data point for generating thefirst Tchebychev polynomial based on (a) the additional failureoccurring within the predetermined time of the one failure of the firstcomputer system and (b) the severity of the one failure of the firstcomputer system being greater than the severity of the additionalfailure.
 7. The computer program product of claim 5, wherein the firstcomputer system comprises a first network of first computers includingfirst software installed in the first computers, and wherein the secondcomputer system comprises a second network of second computers includingsecond software installed in the second computers.
 8. The computerprogram product of claim 5, wherein if time T1min is less than timeT2min then the third Tchebychev polynomial curve passes through thefirst Tchebychev polynomial curve at time T1min; wherein if time T2minis less than time T1min then the third Tchebychev polynomial curvepasses through the second Tchebychev polynomial curve at time T2min;wherein if time T1min is equal to time T2min then the third Tchebychevpolynomial curve passes through whichever Tchebychev polynomial curve ofthe first and second Tchebychev polynomial curves has a higher severityat time T1min; wherein if time T1max is greater than time T2max then thethird Tchebychev polynomial curve passes through the first Tchebychevpolynomial curve at time T1max; wherein if time T2max is greater thantime T1max then the third Tchebychev polynomial curve passes through thesecond Tchebychev polynomial curve at time T2max; wherein if time T1maxis equal to time T2max then the third Tchebychev polynomial curve passesthrough whichever Tchebychev polynomial curve of the first and secondTchebychev polynomial curves has a higher severity at time T1max.
 9. Acomputer, comprising a processor, a memory, and a computer readablestorage device, the storage device containing program instructionsexecutable by the processor via the memory to implement a method ofestimating risk of a future failure of first and second computer systemsof a computer network and taking remedial action which minimizes therisk of the future failure of the first and second computer systems, themethod comprising: the processor identifying, as first coordinates offirst data points, (a) severities of previous, respective failures ofthe first computer system and (b) respective times of occurrences,encompassing a time range from an earliest time of occurrence T1min to alatest time of occurrence T1max, of the previous, respective failures ofthe first computer system, wherein the severities are the firstcoordinates on a severity axis and the respective times of theoccurrences are the first coordinates on a perpendicular time axis; theprocessor generating a first Tchebychev polynomial curve passing throughall of the first data points representing the previous failures of thefirst computer system, and identifying peaks and ends of the firstTchebychev polynomial curve; the processor identifying, as secondcoordinates of second data points, (a) severities of previous,respective failures of the second computer system and (b) respectivetimes of occurrences, encompassing a time range from an earliest time ofoccurrence T2min to a latest time of occurrence T2max, of the previous,respective failures of the second computer system, wherein theseverities are the second coordinates on the severity axis and therespective times of the occurrences are the second coordinates on theperpendicular time axis; the processor generating a second Tchebychevpolynomial curve passing through all of the second data pointsrepresenting the previous failures of the second computer system, andidentifying peaks and ends of the second Tchebychev polynomial curve;and the processor generating a third Tchebychev polynomial curve passingthrough: (i) all of the peaks of both the first Tchebychev polynomialcurve and the second Tchebychev polynomial curve, (ii) the firstTchebychev polynomial curve at time T1min or the second Tchebychevpolynomial curve at time T2min, and (iii) the first Tchebychevpolynomial curve at time T1max or the second Tchebychev polynomial curveat time T2max; and the processor identifying a highest peak of the thirdTchebychev polynomial curve and determining that the identified highestpeak is a high risk failure that occurred on the first or secondcomputer system and is a disaster generating significant risk to thecomputer network and in response, causing other computers of thecomputer network to provide additional redundancy to minimize thesignificant risk to the computer network from a future occurrence of thehigh risk failure of the first and second computer systems.
 10. Thecomputer of claim 9, the method further comprising: the processoridentifying an additional failure of the first computer system, theadditional failure occurring within a predetermined time period of oneof the failures of the first computer system, a severity of the onefailure of the first computer system being greater than a severity ofthe additional failure; and the processor determining not to use theadditional failure as a data point for generating the first Tchebychevpolynomial based on (a) the additional failure occurring within thepredetermined time of the one failure of the first computer system and(b) the severity of the one failure of the first computer system beinggreater than the severity of the additional failure.
 11. The computer ofclaim 9, wherein the first computer system comprises a first network offirst computers including first software installed in the firstcomputers, and wherein the second computer system comprises a secondnetwork of second computers including second software installed in thesecond computers.
 12. The computer of claim 9, wherein if time T1min isless than time T2min then the third Tchebychev polynomial curve passesthrough the first Tchebychev polynomial curve at time T1min; wherein iftime T2min is less than time T1min then the third Tchebychev polynomialcurve passes through the second Tchebychev polynomial curve at timeT2min; wherein if time T1min is equal to time T2min then the thirdTchebychev polynomial curve passes through whichever Tchebychevpolynomial curve of the first and second Tchebychev polynomial curveshas a higher severity at time T1min; wherein if time T1max is greaterthan time T2max then the third Tchebychev polynomial curve passesthrough the first Tchebychev polynomial curve at time T1max; wherein iftime T2max is greater than time T1max then the third Tchebychevpolynomial curve passes through the second Tchebychev polynomial curveat time T2max; wherein if time T1max is equal to time T2max then thethird Tchebychev polynomial curve passes through whichever Tchebychevpolynomial curve of the first and second Tchebychev polynomial curveshas a higher severity at time T1max.